# The Klein Group, Squares of Opposition and the Explanation of Fallacies in Reasoning (2016), p. 386

by Robert, Serge; Brisson, Janie

Copyright according to our policy

### Caption

- KLEIN GROUP 3. The group of tautologies ($\top$) and contradictions ($\bot$)

- Aristotelian family
- Sigma-0 Graph
- Boolean complexity
- 1
- Number of labels per vertex (at most)
- 4
- Equivalence between (some) labels of the same vertex
- Yes
- Analogy between (some) labels of the same vertex
- No
- Uniqueness of the vertices up to logical equivalence
- Yes
- Errors in the diagram
- No
- Shape
- Digon (regular)
- Colinearity range
- 0
- Coplanarity range
- 0
- Cospatiality range
- 0
- Representation of contradiction
- By central symmetry

### Logic

### Geometry

- Conceptual info
- No
- Mnemonic support (AEIO, purpurea ...)
- No
- Form
- none
- Label type
- symbolic
- Symbolic field
- bitstrings ,
- logic
- Contains partial formulas or symbols
- Yes
- Contains protobitstrings
- No
- Bitstring length
- 4
- Logical system
- propositional logic
- Contains definitions of relations
- No
- Form
- solid lines
- Has arrowheads
- No
- Overlap
- No
- Curved
- No
- Hooked
- No
- As wide as vertices
- No
- Contains text
- No
- Label type
- none

### Vertex description

### Edge description

- Diagram is colored
- No
- Diagram is embellished
- No
- Tags
- Boolean closed ;
- non-contingent formulas ;
- duality